Third-order iterative methods for operators with bounded second derivative

THIRD-ORDER AND FOURTH-ORDER ITERATIVE METHODS FREE FROM SECOND DERIVATIVE FOR FINDING MULTIPLE ROOTS OF NONLINEAR EQUATIONS

In this paper, we present two new families of third-order and fourth-order methods for finding multiple roots of nonlinear equations. Each of them requires one evaluation of the function and two of its first derivative per iteration. Several numerical examples are given to illustrate the performance of the presented methods.    

third-order and fourth-order iterative methods free from second derivative for finding multiple roots of nonlinear equations

in this paper, we present two new families of third-order and fourth-order methods for finding multiple roots of nonlinear equations. each of them requires one evaluation of the function and two of its first derivative per iteration. several numerical examples are given to illustrate the performance of the presented methods.

Third order iterative methods free from second derivative for nonlinear systems

In this paper, we present a class of new iterative methods, in which f ′(x) = 0 in some points is permitted. Analysis of convergence shows that the new methods are cubically convergent. Per iteration the new methods require one evaluation of the function and two of its first derivative, but no evaluations of its second derivative. Thus, the new methods have definite practical utility, which is ...

Seventh-order iterative algorithm free from second derivative for solving algebraic nonlinear equations

A Note on Some Higher-Order Iterative Methods Free from Second Derivative for Solving Nonlinear Equations

In the recent paper [M. A. Noor, W. A. Khan, K. I. Noor and Eisa Al-Said, Higher-order iterative methods free from second derivative for solving nonlinear equations, International Journal of the Physical Sciences, Vol. 6 (8) (2011), 1887-1893] several iterative methods for solving nonlinear equations are presented. One of the methods is the three-step iterative method given in Algorithm (2.10) ...